Finite Group Databasebeta

← C7×#24465 #13201681

Subgroups — C7×#24465 #13201681

Order 1792.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3489C211yesmaximal, characteristic, complemented
2C7×#3055C211yesmaximal, characteristic, complemented
3C2×C7×#454C211yesmaximal, characteristic, complemented
4C7×#3006C211yesmaximal, characteristic, complemented
5C22×C7×#104C211yesmaximal, characteristic, complemented
6C7×#2850C211yesmaximal, characteristic, complemented
7C7×#2040C211yesmaximal, characteristic, complemented
8C7×#2038C211yesmaximal, characteristic, complemented
9C7×#2006C211yesmaximal, characteristic, complemented
10C7×#2003C211yesmaximal, characteristic, complemented
11C7×#1901C211yesmaximal, characteristic, complemented
12C7×#1896C211yesmaximal, characteristic, complemented
13C7×#1883C211yesmaximal, characteristic, complemented
14C7×#1860C211yesmaximal, characteristic, complemented
15C7×#1793C211yesmaximal, characteristic, complemented
16C2×C7×2−1+4C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C7×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×C7×M16C2211yescharacteristic
22C7×D4×Q8—21no—
23C7×#548—21no—
24C7×#547—21no—
25C7×#547—22no—
26C7×#546—21no—
27C7×#546—22no—
28C7×#537—21no—
29C7×#537C2211yescharacteristic
30C7×#536—21no—
31C7×#536C2211yescharacteristic
32C2×C7×#124C2211yescharacteristic, complemented
33C7×#525—21no—
34C7×#525C2211yescharacteristic
35C2×C7×C22⋊Q8—21no—
36C2×C7×C22⋊Q8C2211yescharacteristic
37C2×C7×#121C2211yescharacteristic
38C7×#520C2211yescharacteristic
39C22×C42×C7C2211yescharacteristic
40C7×#469—21no—
41C7×#468—21no—
42C7×#466—21no—
43C7×#465—21no—
44C7×#454—24no—
45C7×#449—21no—
46C7×#449—21no—
47C7×#448—21no—
48C7×#447—21no—
49C7×#428C2211yescharacteristic, complemented
50C2×C7×#104—24no—
51C2×C7×#104C2211yescharacteristic
52C2×C7×#104C2211yescharacteristic
53C2×C7×#104C2211yescharacteristic
54C2×C7×#104C2211yescharacteristic
55C2×C7×#104C2211yescharacteristic, complemented
56C2×C7×#104C2211yescharacteristic, complemented
57C7×#418C2211yescharacteristic, complemented
58C7×#417C2211yescharacteristic
59C7×#417C2211yescharacteristic
60C7×#417C2211yescharacteristic, complemented
61C2×C7×#101C2211yescharacteristic, complemented
62C2×C7×#101C2211yescharacteristic, complemented
63C7×#407C2211yescharacteristic
64C7×#391C2211yescharacteristic, complemented
65C7×#390C2211yescharacteristic, complemented
66C7×#388—22no—
67C7×#386—22no—
68C7×#382C2211yescharacteristic, complemented
69C7×#343C2211yescharacteristic, complemented
70C7×#343C2211yescharacteristic, complemented
71C7×#339C2211yescharacteristic, complemented
72C7×#339C2211yescharacteristic, complemented
73#24465C711yesmaximal, characteristic, direct product factor, Sylow
74C7×2−1+4—22no—
75C7×2−1+4—22no—
76C7×2−1+4—41no—
77C7×2−1+4—41no—
78C2×C7×#41—21no—
79C2×C7×#41—21no—
80C2×C7×#41—21no—
81C2×C7×#41—21no—
82C2×C7×#41—22no—
83C2×C7×#41—22no—
84C2×C7×#41—22no—
85C2×C7×#41—41no—
86C2×C7×#41—41no—
87C2×C7×#41D411yescharacteristic
88C2×C7×#41D411yescharacteristic
89C2×C7×#41C2311yescharacteristic
90C2×C7×#41C2311yescharacteristic
91C2×C7×#41C2311yescharacteristic
92C22×C7×Q8—21no—
93C22×C7×Q8—21no—
94C22×C7×Q8D411yescharacteristic
95C22×C7×Q8C2311yescharacteristic
96C22×C7×D4—21no—
97C22×C7×D4—21no—
98C22×C7×D4D411yescharacteristic
99C22×C7×D4C2311yescharacteristic
100C23×C4×C7—21no—
101C23×C4×C7—21no—
102C23×C4×C7C2311yescharacteristic
103C7×AGL(1,ℤ/8)—22no—
104C7×AGL(1,ℤ/8)—22no—
105C7×AGL(1,ℤ/8)—22no—
106C7×AGL(1,ℤ/8)—41no—
107C7×AGL(1,ℤ/8)—41no—
108C7×AGL(1,ℤ/8)—41no—
109C2×C7×SD16—21no—
110C2×C7×SD16—21no—
111C2×C7×SD16—21no—
112C2×C7×D8—21no—
113C2×C7×D8—21no—
114C2×C7×D8—21no—
115C2×C7×M16—21no—
116C2×C7×M16—22no—
117C2×C7×M16—41no—
118C2×C7×M16C2311yescharacteristic
119C2×C7×M16C2311yescharacteristic
120C2×C7×M16C2311yescharacteristic
121C2×C7×M16C2311yescharacteristic
122C22×C7×C8—21no—
123C7×C4⋊Q8—22no—
124C7×C4⋊Q8—21no—
125C7×#124—22no—
126C7×#124—21no—
127C7×#124—22no—
128C7×#124—41no—
129C7×#123—22no—
130C7×#123—22no—
131C7×#123—22no—
132C7×#123—21no—
133C7×#123—22no—
134C7×C22⋊Q8—22no—
135C7×C22⋊Q8—22no—
136C7×C22⋊Q8—22no—
137C7×C22⋊Q8—21no—
138C7×C22⋊Q8—21no—
139C7×C22⋊Q8—21no—
140C7×C22⋊Q8—21no—
141C7×C22⋊Q8—21no—
142C7×C22⋊Q8—21no—
143C7×C22⋊Q8—21no—
144C7×C22⋊Q8—21no—
145C7×C22⋊Q8D411yescharacteristic
146C7×C22⋊Q8D411yescharacteristic
147C7×#121—22no—
148C7×#121—22no—
149C7×#121—22no—
150C7×#121—21no—
151C7×#121—21no—
152C7×#121—22no—
153C7×#121—21no—
154C7×#121—21no—
155C7×#121—21no—
156C7×#121—21no—
157C7×#121D411yescharacteristic
158C7×#121D411yescharacteristic
159C7×#120—22no—
160C7×#120—21no—
161C4×C7×Q8—21no—
162C4×C7×D4—22no—
163C4×C7×D4—22no—
164C4×C7×D4—21no—
165C4×C7×D4—22no—
166C4×C7×D4—21no—
167C4×C7×D4—21no—
168C7×#117—21no—
169C7×#117C2311yescharacteristic
170C2×C7×C4⋊C4—22no—
171C2×C7×C4⋊C4—21no—
172C2×C7×C4⋊C4D412yes—
173C2×C7×C4⋊C4C2311yescharacteristic
174C2×C7×C4⋊C4C2311yescharacteristic
175C2×C7×C22⋊C4—22no—
176C2×C7×C22⋊C4—21no—
177C2×C7×C22⋊C4—22no—
178C2×C7×C22⋊C4—22no—
179C2×C7×C22⋊C4D412yes—
180C2×C42×C7—22no—
181C2×C42×C7—21no—
182C2×C42×C7—41no—
183C2×C42×C7C2311yescharacteristic
184C2×C42×C7C2311yescharacteristic
185C7×#107—21no—
186C7×#106—21no—
187C7×#104—22no—
188C7×#104—22no—
189C7×#104—22no—
190C7×#104—22no—
191C7×#104—41no—
192C7×#104D414yescomplemented
193C7×#103—21no—
194C7×#103—21no—
195C7×#103—21no—
196C7×#102—21no—
197C7×#102—21no—
198C7×#102—21no—
199C7×#102—21no—
200C7×#102—21no—
201C7×#101—22no—
202C7×#101—41no—
203C7×C22⋊C8—21no—
204C7×C22⋊C8—21no—
205C7×#95—22no—
206C7×#95—22no—
207#3489C2×C711yescharacteristic, complemented
208#3055C2×C711yescharacteristic, complemented
209C2×#454C2×C711yescharacteristic, complemented
210#3006C2×C711yescharacteristic, complemented
211C22×#104C2×C711yescharacteristic, complemented
212#2850C2×C711yescharacteristic, complemented
213#2040C2×C711yescharacteristic, complemented
214#2038C2×C711yescharacteristic, complemented
215#2006C2×C711yescharacteristic, complemented
216#2003C2×C711yescharacteristic, complemented
217#1901C2×C711yescharacteristic, complemented
218#1896C2×C711yescharacteristic, complemented
219#1883C2×C711yescharacteristic, complemented
220#1860C2×C711yescharacteristic, complemented
221#1793C2×C711yescharacteristic, complemented
222C24×C7—21no—
223C24×C7—21no—
224C24×C7C2×D411yescharacteristic
225C7×#41—21no—
226C7×#41—21no—
227C7×#41—22no—
228C7×#41—22no—
229C7×#41—21no—
230C7×#41—21no—
231C7×#41—21no—
232C7×#41—21no—
233C7×#41—21no—
234C7×#41—21no—
235C7×#41—21no—
236C7×#41—21no—
237C7×#41—42no—
238C7×#41—42no—
239C7×#41—41no—
240C7×#41—41no—
241C7×#41—42no—
242C7×#41—42no—
243C7×#41—42no—
244C7×#41—42no—
245C7×#41—44no—
246C7×#41—44no—
247C7×#41—42no—
248C7×#41—42no—
249C7×#41C2×D412yes—
250C7×#41#4112yes—
251C2×C7×Q8—22no—
252C2×C7×Q8—21no—
253C2×C7×Q8—21no—
254C2×C7×Q8—21no—
255C2×C7×Q8—21no—
256C2×C7×Q8—21no—
257C2×C7×Q8—21no—
258C2×C7×Q8—21no—
259C2×C7×Q8—22no—
260C2×C7×Q8—41no—
261C2×C7×Q8—42no—
262C2×C7×Q8—42no—
263C2×C7×Q8—42no—
264C2×C7×Q8—42no—
265C2×C7×Q8C2×D411yescharacteristic
266C2×C7×Q8C2×D411yescharacteristic
267C2×C7×Q8C2×D411yescharacteristic
268C2×C7×D4—21no—
269C2×C7×D4—22no—
270C2×C7×D4—22no—
271C2×C7×D4—21no—
272C2×C7×D4—21no—
273C2×C7×D4—21no—
274C2×C7×D4—21no—
275C2×C7×D4—21no—
276C2×C7×D4—22no—
277C2×C7×D4—21no—
278C2×C7×D4—21no—
279C2×C7×D4—21no—
280C2×C7×D4—21no—
281C2×C7×D4—21no—
282C2×C7×D4—21no—
283C2×C7×D4—21no—
284C2×C7×D4—21no—
285C2×C7×D4—41no—
286C2×C7×D4—42no—
287C2×C7×D4—42no—
288C2×C7×D4—44no—
289C2×C7×D4—41no—
290C2×C7×D4—41no—
291C2×C7×D4C2×D411yescharacteristic
292C2×C7×D4C2×D411yescharacteristic
293C2×C7×D4C2×D411yescharacteristic
294C22×C4×C7—21no—
295C22×C4×C7—21no—
296C22×C4×C7—21no—
297C22×C4×C7—21no—
298C22×C4×C7—21no—
299C22×C4×C7—22no—
300C22×C4×C7—22no—
301C22×C4×C7—21no—
302C22×C4×C7—21no—
303C22×C4×C7—21no—
304C22×C4×C7—22no—
305C22×C4×C7—21no—
306C22×C4×C7—21no—
307C22×C4×C7—21no—
308C22×C4×C7—21no—
309C22×C4×C7—21no—
310C22×C4×C7—42no—
311C22×C4×C7—42no—
312C22×C4×C7—42no—
313C22×C4×C7—42no—
314C22×C4×C7—42no—
315C22×C4×C7C2×D412yes—
316C22×C4×C7C2×D411yescharacteristic
317C22×C4×C7C2×D411yescharacteristic
318C22×C4×C7C2×D411yescharacteristic
319C22×C4×C7C2×D411yescharacteristic
320C22×C4×C7C2×D411yescharacteristic
321C22×C4×C7C2×D412yes—
322C22×C4×C7C2411yescharacteristic
323C7×SD16—42no—
324C7×SD16—42no—
325C7×SD16—42no—
326C7×D8—42no—
327C7×D8—42no—
328C7×D8—42no—
329C7×M16—21no—
330C7×M16—21no—
331C7×M16—21no—
332C7×M16—21no—
333C7×M16—21no—
334C7×M16—21no—
335C7×M16—21no—
336C7×M16—42no—
337C7×M16C2×D412yes—
338C2×C7×C8—21no—
339C2×C7×C8—21no—
340C2×C7×C8—21no—
341C2×C7×C8—21no—
342C2×C7×C8—42no—
343C7×C4⋊C4—22no—
344C7×C4⋊C4—22no—
345C7×C4⋊C4—22no—
346C7×C4⋊C4—22no—
347C7×C4⋊C4—21no—
348C7×C4⋊C4—22no—
349C7×C4⋊C4—22no—
350C7×C4⋊C4—21no—
351C7×C4⋊C4—21no—
352C7×C4⋊C4—21no—
353C7×C4⋊C4—21no—
354C7×C4⋊C4—21no—
355C7×C4⋊C4C2×D411yescharacteristic
356C7×C4⋊C4C2×D411yescharacteristic
357C7×C22⋊C4—22no—
358C7×C22⋊C4—22no—
359C7×C22⋊C4—22no—
360C7×C22⋊C4—22no—
361C7×C22⋊C4—22no—
362C7×C22⋊C4—21no—
363C7×C22⋊C4—22no—
364C7×C22⋊C4—22no—
365C7×C22⋊C4—21no—
366C7×C22⋊C4—21no—
367C7×C22⋊C4—21no—
368C7×C22⋊C4—21no—
369C7×C22⋊C4—44no—
370C7×C22⋊C4—44no—
371C7×C22⋊C4—41no—
372C7×C22⋊C4—41no—
373C42×C7—22no—
374C42×C7—21no—
375C42×C7—21no—
376C42×C7—21no—
377C42×C7—21no—
378C42×C7—42no—
379C42×C7C2×D412yes—
380C2×2−1+4C22×C711yescharacteristic
381C22×#41C22×C711yescharacteristic
382C2×AGL(1,ℤ/8)C22×C711yescharacteristic
383C2×AGL(1,ℤ/8)C22×C711yescharacteristic
384C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
385C22×M16C22×C711yescharacteristic
386D4×Q8—21no—
387#548—21no—
388#547—21no—
389#547—22no—
390#546—21no—
391#546—22no—
392#537—21no—
393#537C22×C711yescharacteristic
394#536—21no—
395#536C22×C711yescharacteristic
396C2×#124C22×C711yescharacteristic, complemented
397#525—21no—
398#525C22×C711yescharacteristic
399C2×C22⋊Q8—21no—
400C2×C22⋊Q8C22×C711yescharacteristic
401C2×#121C22×C711yescharacteristic
402#520C22×C711yescharacteristic
403C22×C42C22×C711yescharacteristic
404#469—21no—
405#468—21no—
406#466—21no—
407#465—21no—
408#454—24no—
409#449—21no—
410#449—21no—
411#448—21no—
412#447—21no—
413#428C22×C711yescharacteristic, complemented
414C2×#104—24no—
415C2×#104C22×C711yescharacteristic
416C2×#104C22×C711yescharacteristic
417C2×#104C22×C711yescharacteristic
418C2×#104C22×C711yescharacteristic
419C2×#104C22×C711yescharacteristic, complemented
420C2×#104C22×C711yescharacteristic, complemented
421#418C22×C711yescharacteristic, complemented
422#417C22×C711yescharacteristic
423#417C22×C711yescharacteristic
424#417C22×C711yescharacteristic, complemented
425C2×#101C22×C711yescharacteristic, complemented
426C2×#101C22×C711yescharacteristic, complemented
427#407C22×C711yescharacteristic
428#391C22×C711yescharacteristic, complemented
429#390C22×C711yescharacteristic, complemented
430#388—22no—
431#386—22no—
432#382C22×C711yescharacteristic, complemented
433#343C22×C711yescharacteristic, complemented
434#343C22×C711yescharacteristic, complemented
435#339C22×C711yescharacteristic, complemented
436#339C22×C711yescharacteristic, complemented
437C23×C7—21no—
438C23×C7—21no—
439C23×C7—21no—
440C23×C7—22no—
441C23×C7—21no—
442C23×C7—21no—
443C23×C7—41no—
444C23×C7—42no—
445C23×C7—42no—
446C23×C7—42no—
447C23×C7—42no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—41no—
451C23×C7—81no—
452C23×C7#12011yescharacteristic
453C23×C7#12011yescharacteristic
454C23×C7C22×D411yescharacteristic
455C7×Q8—21no—
456C7×Q8—21no—
457C7×Q8—21no—
458C7×Q8—21no—
459C7×Q8—21no—
460C7×Q8—42no—
461C7×Q8—44no—
462C7×Q8—41no—
463C7×Q8—41no—
464C7×Q8—41no—
465C7×Q8—41no—
466C7×Q8#12112yes—
467C7×D4—22no—
468C7×D4—22no—
469C7×D4—21no—
470C7×D4—21no—
471C7×D4—21no—
472C7×D4—21no—
473C7×D4—21no—
474C7×D4—42no—
475C7×D4—42no—
476C7×D4—42no—
477C7×D4—44no—
478C7×D4—41no—
479C7×D4—41no—
480C7×D4—41no—
481C7×D4—41no—
482C7×D4—42no—
483C7×D4—41no—
484C7×D4—41no—
485C7×D4—41no—
486C7×D4—41no—
487C7×D4—81no—
488C7×D4—82no—
489C7×D4—82no—
490C7×D4—82no—
491C7×D4#12112yes—
492C2×C4×C7—21no—
493C2×C4×C7—21no—
494C2×C4×C7—21no—
495C2×C4×C7—21no—
496C2×C4×C7—21no—
497C2×C4×C7—21no—
498C2×C4×C7—21no—
499C2×C4×C7—21no—
500C2×C4×C7—21no—
501C2×C4×C7—22no—
502C2×C4×C7—21no—
503C2×C4×C7—21no—
504C2×C4×C7—22no—
505C2×C4×C7—22no—
506C2×C4×C7—21no—
507C2×C4×C7—22no—
508C2×C4×C7—21no—
509C2×C4×C7—21no—
510C2×C4×C7—22no—
511C2×C4×C7—21no—
512C2×C4×C7—22no—
513C2×C4×C7—22no—
514C2×C4×C7—22no—
515C2×C4×C7—42no—
516C2×C4×C7—42no—
517C2×C4×C7—42no—
518C2×C4×C7—44no—
519C2×C4×C7—41no—
520C2×C4×C7—41no—
521C2×C4×C7—41no—
522C2×C4×C7—44no—
523C2×C4×C7—48no—
524C2×C4×C7—41no—
525C2×C4×C7—41no—
526C2×C4×C7—41no—
527C2×C4×C7—41no—
528C2×C4×C7—41no—
529C2×C4×C7—42no—
530C2×C4×C7—42no—
531C2×C4×C7—41no—
532C2×C4×C7—82no—
533C2×C4×C7#12011yescharacteristic
534C2×C4×C7#12011yescharacteristic
535C2×C4×C7C22×D411yescharacteristic
536C2×C4×C7C22×D411yescharacteristic
537C2×C4×C7C22×D411yescharacteristic
538C2×C4×C7C2×#4111yescharacteristic
539C2×C4×C7H(5,𝔽2)11yescharacteristic
540C2×C4×C7H(5,𝔽2)11yescharacteristic
541C7×C8—22no—
542C7×C8—41no—
543C7×C8—41no—
544C7×C8—41no—
5452−1+4—22no—
5462−1+4—22no—
5472−1+4—41no—
5482−1+4—41no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—22no—
553C2×#41—21no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41C7×D411yescharacteristic
559C2×#41C7×D411yescharacteristic
560C2×#41C23×C711yescharacteristic
561C2×#41C23×C711yescharacteristic
562C2×#41C23×C711yescharacteristic
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8C7×D411yescharacteristic
566C22×Q8C23×C711yescharacteristic
567C22×D4—21no—
568C22×D4—21no—
569C22×D4C7×D411yescharacteristic
570C22×D4C23×C711yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C711yescharacteristic
574AGL(1,ℤ/8)—22no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)—22no—
577AGL(1,ℤ/8)—41no—
578AGL(1,ℤ/8)—41no—
579AGL(1,ℤ/8)—41no—
580C2×SD16—21no—
581C2×SD16—21no—
582C2×SD16—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×M16—21no—
587C2×M16—22no—
588C2×M16—41no—
589C2×M16C23×C711yescharacteristic
590C2×M16C23×C711yescharacteristic
591C2×M16C23×C711yescharacteristic
592C2×M16C23×C711yescharacteristic
593C22×C8—21no—
594C4⋊Q8—22no—
595C4⋊Q8—21no—
596#124—22no—
597#124—21no—
598#124—22no—
599#124—41no—
600#123—22no—
601#123—22no—
602#123—22no—
603#123—21no—
604#123—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8—21no—
615C22⋊Q8—21no—
616C22⋊Q8C7×D411yescharacteristic
617C22⋊Q8C7×D411yescharacteristic
618#121—22no—
619#121—22no—
620#121—22no—
621#121—21no—
622#121—21no—
623#121—22no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121C7×D411yescharacteristic
629#121C7×D411yescharacteristic
630#120—22no—
631#120—21no—
632C4×Q8—21no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—21no—
636C4×D4—22no—
637C4×D4—21no—
638C4×D4—21no—
639#117—21no—
640#117C23×C711yescharacteristic
641C2×C4⋊C4—22no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4C7×D412yes—
644C2×C4⋊C4C23×C711yescharacteristic
645C2×C4⋊C4C23×C711yescharacteristic
646C2×C22⋊C4—22no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4C7×D412yes—
651C2×C42—22no—
652C2×C42—21no—
653C2×C42—41no—
654C2×C42C23×C711yescharacteristic
655C2×C42C23×C711yescharacteristic
656#107—21no—
657#106—21no—
658#104—22no—
659#104—22no—
660#104—22no—
661#104—22no—
662#104—41no—
663#104C7×D414yescomplemented
664#103—21no—
665#103—21no—
666#103—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671#102—21no—
672#101—22no—
673#101—41no—
674C22⋊C8—21no—
675C22⋊C8—21no—
676#95—22no—
677#95—22no—
678C22×C7—21no—
679C22×C7—21no—
680C22×C7—21no—
681C22×C7—21no—
682C22×C7—21no—
683C22×C7—22no—
684C22×C7—21no—
685C22×C7—21no—
686C22×C7—42no—
687C22×C7—42no—
688C22×C7—41no—
689C22×C7—41no—
690C22×C7—41no—
691C22×C7—41no—
692C22×C7—41no—
693C22×C7—41no—
694C22×C7—41no—
695C22×C7—41no—
696C22×C7—84no—
697C22×C7—82no—
698C22×C7—82no—
699C22×C7—81no—
700C22×C7—81no—
701C22×C7—81no—
702C22×C7#45412yescomplemented
703C22×C7C2×#12011yescharacteristic
704C22×C7D4211yescharacteristic
705C22×C7#54611yescharacteristic
706C4×C7—21no—
707C4×C7—21no—
708C4×C7—22no—
709C4×C7—42no—
710C4×C7—42no—
711C4×C7—42no—
712C4×C7—41no—
713C4×C7—41no—
714C4×C7—41no—
715C4×C7—42no—
716C4×C7—41no—
717C4×C7—81no—
718C4×C7C2×#12111yescharacteristic
719C4×C7#53411yescharacteristic
720C4×C7D4211yescharacteristic
721C4×C7#54611yescharacteristic
722C24—21no—
723C24—21no—
724C24C2×C7×D411yescharacteristic
725#41—21no—
726#41—21no—
727#41—22no—
728#41—22no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—41no—
740#41—41no—
741#41—42no—
742#41—42no—
743#41—42no—
744#41—42no—
745#41—44no—
746#41—44no—
747#41—42no—
748#41—42no—
749#41C2×C7×D412yes—
750#41C7×#4112yes—
751C2×Q8—22no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—22no—
760C2×Q8—41no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8C2×C7×D411yescharacteristic
766C2×Q8C2×C7×D411yescharacteristic
767C2×Q8C2×C7×D411yescharacteristic
768C2×D4—21no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—22no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—41no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—44no—
789C2×D4—41no—
790C2×D4—41no—
791C2×D4C2×C7×D411yescharacteristic
792C2×D4C2×C7×D411yescharacteristic
793C2×D4C2×C7×D411yescharacteristic
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4C2×C7×D412yes—
816C22×C4C2×C7×D411yescharacteristic
817C22×C4C2×C7×D411yescharacteristic
818C22×C4C2×C7×D411yescharacteristic
819C22×C4C2×C7×D411yescharacteristic
820C22×C4C2×C7×D411yescharacteristic
821C22×C4C2×C7×D412yes—
822C22×C4C24×C711yescharacteristic
823SD16—42no—
824SD16—42no—
825SD16—42no—
826D8—42no—
827D8—42no—
828D8—42no—
829M16—21no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16—42no—
837M16C2×C7×D412yes—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—42no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—21no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4C2×C7×D411yescharacteristic
856C4⋊C4C2×C7×D411yescharacteristic
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—21no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—41no—
872C22⋊C4—41no—
873C42—22no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—42no—
879C42C2×C7×D412yes—
880C2×C7—21no—
881C2×C7—21no—
882C2×C7—22no—
883C2×C7—41no—
884C2×C7—42no—
885C2×C7—81no—
886C2×C7—81no—
887C2×C7—161no—
888C2×C7#241011yescharacteristic
889C2×C7C2×#45411yescharacteristic
890C2×C7#301811yescharacteristic
891C23—21no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—81no—
906C23C7×#12011yescharacteristic
907C23C7×#12011yescharacteristic
908C23C22×C7×D411yescharacteristic
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—21no—
913Q8—21no—
914Q8—42no—
915Q8—44no—
916Q8—41no—
917Q8—41no—
918Q8—41no—
919Q8—41no—
920Q8C7×#12112yes—
921D4—22no—
922D4—22no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—21no—
927D4—21no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—44no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—42no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—81no—
942D4—82no—
943D4—82no—
944D4—82no—
945D4C7×#12112yes—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—44no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—44no—
977C2×C4—48no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—41no—
986C2×C4—82no—
987C2×C4C7×#12011yescharacteristic
988C2×C4C7×#12011yescharacteristic
989C2×C4C22×C7×D411yescharacteristic
990C2×C4C22×C7×D411yescharacteristic
991C2×C4C22×C7×D411yescharacteristic
992C2×C4C2×C7×#4111yescharacteristic
993C2×C4C7×H(5,𝔽2)11yescharacteristic
994C2×C4C7×H(5,𝔽2)11yescharacteristic
995C8—22no—
996C8—41no—
997C8—41no—
998C8—41no—
999C7#2446511yescharacteristic, direct product factor, Sylow
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—22no—
1006C22—21no—
1007C22—21no—
1008C22—42no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22C7×#45412yescomplemented
1025C22C2×C7×#12011yescharacteristic
1026C22C7×D4211yescharacteristic
1027C22C7×#54611yescharacteristic
1028C4—21no—
1029C4—21no—
1030C4—22no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—81no—
1040C4C2×C7×#12111yescharacteristic
1041C4C7×#53411yescharacteristic
1042C4C7×D4211yescharacteristic
1043C4C7×#54611yescharacteristic
1044C2—21no—
1045C2—21no—
1046C2—22no—
1047C2—41no—
1048C2—42no—
1049C2—81no—
1050C2—81no—
1051C2—161no—
1052C2C7×#241011yescharacteristic
1053C2C2×C7×#45411yescharacteristic
1054C2C7×#301811yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C7×#3489C2semidirect
2. C7×#3055C2semidirect
3. C2×C7×#454C2semidirect
4. C7×#3006C2semidirect
5. C22×C7×#104C2semidirect
6. C7×#2850C2semidirect
7. C7×#2040C2semidirect
8. C7×#2038C2semidirect
9. C7×#2006C2semidirect
10. C7×#2003C2semidirect
11. C7×#1901C2semidirect
12. C7×#1896C2semidirect
13. C7×#1883C2semidirect
14. C7×#1860C2semidirect
15. C7×#1793C2semidirect
20. C2×C7×AGL(1,ℤ/8)C22semidirect
32. C2×C7×#124C22semidirect
49. C7×#428C22semidirect
55. C2×C7×#104C22semidirect
56. C2×C7×#104C22semidirect
57. C7×#418C22semidirect
60. C7×#417C22semidirect
61. C2×C7×#101C22semidirect
62. C2×C7×#101C22semidirect
64. C7×#391C22semidirect
65. C7×#390C22semidirect
68. C7×#382C22semidirect
69. C7×#343C22semidirect
70. C7×#343C22semidirect
71. C7×#339C22semidirect
72. C7×#339C22semidirect
73. #24465C7direct (N × H)
192. C7×#104D4semidirect
207. #3489C2×C7semidirect
208. #3055C2×C7semidirect
209. C2×#454C2×C7semidirect
210. #3006C2×C7semidirect
211. C22×#104C2×C7semidirect
212. #2850C2×C7semidirect
213. #2040C2×C7semidirect
214. #2038C2×C7semidirect
215. #2006C2×C7semidirect
216. #2003C2×C7semidirect
217. #1901C2×C7semidirect
218. #1896C2×C7semidirect
219. #1883C2×C7semidirect
220. #1860C2×C7semidirect
221. #1793C2×C7semidirect
384. C2×AGL(1,ℤ/8)C22×C7semidirect
396. C2×#124C22×C7semidirect
413. #428C22×C7semidirect
419. C2×#104C22×C7semidirect
420. C2×#104C22×C7semidirect
421. #418C22×C7semidirect
424. #417C22×C7semidirect
425. C2×#101C22×C7semidirect
426. C2×#101C22×C7semidirect
428. #391C22×C7semidirect
429. #390C22×C7semidirect
432. #382C22×C7semidirect
433. #343C22×C7semidirect
434. #343C22×C7semidirect
435. #339C22×C7semidirect
436. #339C22×C7semidirect
663. #104C7×D4semidirect
702. C22×C7#454semidirect
999. C7#24465direct (N × H)
1024. C22C7×#454semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×#34892
C7×#30552
C2×C7×#4542
C7×#30062
C22×C7×#1042
C7×#28502
C7×#20402
C7×#20382
C7×#20062
C7×#20032
C7×#19012
C7×#18962
C7×#18832
C7×#18602
C7×#17932
#244657